Unmanned aerial vehicles (UAVs) with flexible deployment contribute to enlarging the distance of information transmission to mobile users (MUs) in constrained environment. However, due to the high mobility of both UAVs and MUs, it is challenging to establish an accurate beam towards the target MU with high beam gain in real-time. In this study, UAV base stations (UAV-BSs) consisting of position-known assisted UAVs (A-UAVs) and position-unknown assisted UAVs (U-UAVs) are employed to transmit data to MUs. Specifically, a bi-directional angle-aware beam tracking with adaptive beam reconstruction (BAB-AR) algorithm is proposed to construct an optimal beam that can quickly adapt the movement of the target MU. First, the angle-aware beam tracking is realized within the UAVBSs using a proposed global dynamic crow search algorithm without historical trajectory. Furthermore, the Gaussian process regression model is trained by A-UAVs to predict the azimuth and elevation angles of MUs. Meanwhile, we focus on the beam width and design a time interval adjustment mechanism for adaptive beam reconstruction to track high-speed MUs. Finally, the performance of the BAB-AR algorithm is compared with that of benchmark algorithms, and simulate results verifies that the BAB-AR algorithm can construct an accurate beam capable of covering high-speed MUs with the half power beam width in a timely manner.